6. (a) (4 points) What is the dimension of the space S = {(a,b,c,d) a+c+d =...
10 a) Find a basis and the dimension of the row space. b) Find a basis and the dimension of the column space. c) Find a basis and the dimension of the null space. d) Verify the Dimension Theorem for A e) Identify the Domain and Codomain if this is the standard matrix for a linear transformation f) What does the row space represent when this is viewed as a linear transformation? g) Does this represent a linear operator? Explain....
appreciate a clear explanation .tks (thumbup) 1 23 -3 6 7 1 1 2-1 2 4 2 24-2 4 8 (a) Determine the vectors that are in the solution space of A (b) What is the rank of A? (c) What is the dimension of the solution space of A? (d) Determine the vectors that are in the column space of A 13 10 1 23 -3 6 7 1 1 2-1 2 4 2 24-2 4 8 (a) Determine...
Please Explain..... Thank you (gg) What is the maximum possible dimension of the row space of A if A is a 6 x 4 (hh) What is the maximum possible dimension of the column space of A if A is a 6 x 8 What is the change of basis matrix from B2 (jj) Let Bi-{귤1. 귤2). B2-{귤2.3귤ì } . What is the change of basis matrix from B2 matrix? matrixLet B.-{а, и,ls,-ui,.sital to Bi? to B1? (gg) What is...
2 3 4 1 0 6 7 0 6. Find the dimension of the column space of A 4 6 8 2
The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax 0?
Determine with explanation the dimension of (a) complex as a vector space over complex (b) complex as a vector space over reals (c) complex ^3 as a vector over complex (d) complex ^3 as a vector space over reals. I am thinking the following: (a) dim=1:Complex numbers are in the form of a+bi so hence dimension = 1? (b) dim =2: There are two part hence dimension is 2. (c) dim = 3: Complex numbers are in the form of...
2. (6 points). Consider a state space system: C1 =22 22 = - 2.c 1 - 3.02 y=21 +22 Eco with Xo = (-1,1). (a) Specify the state space matrices (A,B,C,D). (b) Compute the matrix exponential eAl using similarity transformation. (e) Find the complete state response (solution of the SS system x(t)) if u(t) = 1. (d) Find the output response y(t) = Cx(t).
4. Let B be a matrix such that -2a -3b nullspace(B)- What is the dimension of the column space of B? What is the dimension of the row space of B?
If the null space of a 6x 12 matrix A is 6-dimensional, what is the dimension of the column space of A? dim Col A= (Simplify your answer.)
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a) Prove that W, is the set of all vector8 α in V such that (T-cd)"a-0 for some positive integer 'n (which may depend upon α). (b) Prove that the dimension of W, is di. (Hint: If T, is the operator induced on Wi by T, then...